by
Xinyu Fang
B.Sc., Beijing University of Technology, 2011
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
MASTER OF APPLIED SCIENCE
in the Department of Electrical and Computer Engineering
c
Xinyu Fang, 2018 University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by photocopying or other means, without the permission of the author.
Xinyu Fang
B.Sc., Beijing University of Technology, 2011
Supervisory Committee
Dr. T. Aaron Gulliver, Supervisor
(Department of Electrical and Computer Engineering)
Dr. Wu-Sheng Lu, Committee Member
Supervisory Committee
Dr. T. Aaron Gulliver, Supervisor
(Department of Electrical and Computer Engineering)
Dr. Wu-Sheng Lu, Committee Member
(Department of Electrical and Computer Engineering)
ABSTRACT
Smart meters (SMs) are key components of the smart grid (SG) as they gather elec-trical usage data from residences and businesses. Home area networks (HANs) are used to provide two-way communications between SMs and devices within a building such as appliances. This can be implemented using power line communications (PLCs) on home wiring topologies. In this thesis, a HAN PLC channel model is designed based on a split-phase power system which includes branch circuits, a panel with circuit breakers and bars, a secondary transformer and the wiring of neighboring residences. A cell division (CD) method is employed to construct the channel model. Further, arc fault circuit interrupter (AFCI) and ground fault circuit interrupter (GFCI) circuit breaker models are developed. Several PLC channels are presented and compared with those obtained using existing mod-els. PLC communication systems are affected by noise, thus a noise model is developed which is comprised of background and impulse noise. This noise model can be used to obtain the noise power spectral density (PSD) at receivers in the wiring topology.
Contents
Supervisory Committee ii
Abstract iii
Table of Contents iv
List of Tables vi
List of Figures vii
List of Abbreviations ix
1 Introduction 1
1.1 Power Line Communications for Home Area Networks . . . 2
1.2 Organization of the Thesis . . . 4
1.3 Contributions . . . 5
2 HAN Topology Modeling 6 2.1 Wiring Topology . . . 6
2.2 Modeling Branch Circuits and Above the Panel . . . 9
2.3 Modeling the Topology Inside the Panel . . . 15
2.4 Cell Division Method . . . 16
3 Model Analysis And Validation 23 3.1 Topology Parameters . . . 23
3.2 Channel Modeling and Analysis . . . 24
3.3 Comparison of Channel Models . . . 28
4 Noise Characterization 33 4.1 Noise Modeling Examples . . . 35
4.1.1 Background Noise . . . 35 4.1.2 Impulse Noise . . . 36
5 Conclusions 40
A The Inner Self Inductance of a Circular or Rectangular Conductor 42
List of Tables
Table 2.1 Appliance Parameters . . . 9
Table 2.2 Properties of Conductors . . . 11
Table 2.3 Parameters of Rectangular Conductors in the Panel . . . 16
Table 3.1 Parameters for the Three House Sizes . . . 25
Table 3.2 Average IL for the Three House Sizes . . . 26
Table 3.3 Average IL of the Three Parts of the Home Topology . . . 28
Table 3.4 Parameters for Three Appliances . . . 29
Table 4.1 Distribution of a . . . 35
Table 4.2 Distribution of fi . . . 37
Table 4.3 Impulse Noise Parameters . . . 37
Table 4.4 Power Spectral Density Differences Between (4.3) and (4.6) at the Impulse Noise Peaks . . . 38
List of Figures
Figure 1.1 The average power consumption of residences. . . 2
Figure 1.2 An impedance carry back method [23] example. . . 4
Figure 2.1 The topology above the panel which includes the smart meter. . . 7
Figure 2.2 The topology of a 200 A Homeline panel. . . 8
Figure 2.3 AWG 6, 3 and 2/0 conductor strands. . . 11
Figure 2.4 Homeline breakers with ratings (a) 200 A and (b) 30 A and 20 A. . . 17
Figure 2.5 The circuit breaker model. . . 18
Figure 2.6 Impedance computation directions of the CD method. . . 19
Figure 2.7 A small appliance circuit cell. . . 20
Figure 2.8 The steps for cell modeling using the cell division method. . . 21
Figure 2.9 A simple topology divided into cells. . . 22
Figure 3.1 The IL of 15 channels from two different medium size house topolo-gies. . . 26
Figure 3.2 The average IL of the channels in the 1000 topologies for each house size. . . 27
Figure 3.3 Average IL of the three parts of the home topology. . . 27
Figure 3.4 The average IL of the 9000 individual circuit channels and the 8000 SA circuit channels in the 1000 topologies. . . 28
Figure 3.5 The average IL with normal breakers and AFCI and GFCI breakers. . 29
Figure 3.6 The Ca˜nete wiring topology modeled using (a) the ABCD matrix method, and (b) the cell division method. . . 30
Figure 3.7 The impedances of the three appliances. . . 31
Figure 3.8 The TFs of four conductors. . . 32
Figure 3.9 The TFs obtained using the ABCD and cell division methods. . . 32
Figure 4.1 The classification of PLC noise [51]. . . 34
and (b) otherwise. . . 42 Figure A.2 A rectangular conductor when (a) the skin depth is greater than half
List of Abbreviations
2PN Two-Port Network
AFCI Arc Fault Circuit Interrupter
AWG American Wire Gauge
AWGN Additive White Gaussian Noise
BB BroadBand
BB-PLC BroadBand Power Line Communication
BPL Broadband over Power Line
BPSK Binary Phase Shift Keying
BSL Bedroom, Study and Living Room
CD Cell Division
CDF Cumulative Distribution Function
CSMA Carrier Sense Multiple Access
CSMA/CA Carrier Sense Multiple Access with Collision Avoidance
CTF Channel Transfer Function
DAC Data Acquisition Center
DER Distributed Energy Resource
DOE Department Of Energy
FSK Frequency Shift Keying
GFCI Ground Fault Circuit Interrupter
HAN Home Area Network
HVAC Heating, Ventilation and Air Conditioning
ICB Impedance Carry Back
IL Insertion Loss
J-J Junction To Junction
J-U Junction To Unknown
LPTV Linear Periodically Time Varying
LTI Linear Time Invariant
MIMO Multiple-Input Multiple-Output
NB NarrowBand
NB-PLC NarrowBand Power Line Communication
NEC National Electric Code
OFDM Orthogonal Frequency Division Multiplexing
p.u.l. Per Unit Length
PDF Probability Density Function
PLC Power Line Communication
PSD Power Spectral Density
QOS Quality of Service
RMS Root Mean Square
RTP Real Time Pricing
Rx Receiver
S-FSK Spread Frequency Shift Keying
SA Small Appliance
SER Service Entrance Cable
SG Smart Grid
SH Smart Home
SISO Single-Input Single-Output
SIMO Single-Input Multiple-Output
SM Smart Meter
SMPS Switched-Mode Power Supply
SS Spread Spectrum
std Standard Deviation
TDMA Time Division Multiple Access
TF Transfer Function
Introduction
Increasing energy demands have resulted in increased greenhouse gas emissions. Govern-ments are now taking efforts to combat climate change and adjust to its effects [1]. One of the approaches is to modernize the electric grid infrastructure and use renewable energy sources [2]. These distributed energy resources (DERs) require communication channels for the management of power transmission and distribution. A power grid with commu-nication techniques to meet these purposes is often referred as a smart grid (SG) [3–5]. Smart meters (SMs) are part of the smart grid which are deployed at residences in place of traditional electric meters.
In North America and Europe, the legislative approval of smart meters has led to an in-crease in the number of intelligent devices such as smart appliances with a growing market of billions of dollars [6, 7]. One of the purposes of SMs is to help both power suppli-ers and residence ownsuppli-ers with power management. Figure 1.1 shows the average power consumption of residences according to the survey by U.S. Department of Energy (DOE) in September 2017. The appliances for heating, ventilation and air conditioning (HVAC) and water heating account for approximately half of the power consumed. A smart meter installed in a residence can provide flexibility in managing these appliances to reduce costs. Smart meters employ bidirectional communications in a smart grid. They can transmit data to data acquisition centers (DACs) for analysis and receive real time pricing informa-tion from the DACs. In a home area network (HAN), SMs collect power usage data from home appliances, send commands to control these appliances, and exchange information with the home owners. Real time pricing (RTP) can be implemented according to recom-mendations by power suppliers so appliances such as dishwashers, washing machines and dryers can be scheduled to operate during off-peak times when prices are low [8]. HVACs and water heaters can be run according to RTP either. Energy theft prevention is another
Figure 1.1: The average power consumption of residences.
function of SMs. With advanced theft detection and encryption algorithms, SMs can detect and report, as well as prevent illegal electricity usage [9]. Appliance monitoring can also be provided by regularly checking and reporting the status of appliances. SMs also benefit power suppliers as remote meter reading is more cost effective than manual reading.
1.1
Power Line Communications for Home Area Networks
The growing interest in smart home (SH) services has prompted research on broadband power line communication (BB-PLC) for high-speed data transmissions. IEEE Std 1901-2010 provides networking protocols for broadband over power line (BPL) devices [10]. IEEE Std 1901.2-2013 for narrowband power line communication (NB-PLC) assures co-existence with the broadband standard [11]. NB-PLC is suitable for the collection of power usage data, and so can be used to provide SM services within businesses and residences via HANs. Modulation schemes for PLC communications include binary phase shift key-ing (BPSK), frequency shift keykey-ing (FSK), spread frequency shift keykey-ing (S-FSK), spread spectrum (SS), orthogonal frequency division multiplexing (OFDM) or a combination of these techniques [12]. Media access control (MAC) protocols include carrier sense multiple access (CSMA) with collision avoidance (CSMA/CA) and time division multiple access (T-DMA). Single-input single-output (SISO), single-input output (SIMO), multiple-input single-output (MISO) and multiple-multiple-input multiple-output (MIMO) techniques have been developed for wireless systems, but are not included in the IEEE BB-PLC and
NB-PLC standards.
Previous research on PLC based smart metering has focused on the links between SMs and DACs [13–16]. However, there has been little research on PLC for HANs. Thus, further study is required. Complex home wiring topologies can be characterized using the components to obtain accurate channel models. Several channel models have been proposed in the literature for this purpose. In [17], a channel model was developed based on a National Electrical Code (NEC) compliant topology. However, the model was constructed as a cascaded two-port network (2PN) with the same path loss in the phase and neutral conductors, which is not realistic. In [18–20], a model of a PLC system with a panel was given, but within the panel, only the bonding strap to the ground was included, so this model is incomplete. The model in [21] used the physical characteristics of conductors, appliances and outlets. However, only part of the panel was considered along with five branch circuits, which is insufficient to model a HAN network. In [22], the influence of circuit breakers on PLC channel models was investigated. Both normal and ground fault circuit interrupter (GFCI) breakers were considered. However, results were based using only measurements and so the results are not general.
The impedance carry back (ICB) method in [23] can be used to develop a HAN channel model. Figure 1.2 shows the steps of this method for a simple example. The backbone refers to the direct path between the transmitter and receiver, while the outlets o1, o2and o3,
and nodes n1and n2 are on an indirect path which is connected to the backbone at nb. The
impedance of this path is calculated from o1 and o2to n2, and finally to nb as illustrated in
Figs. 3(a) to 3(c). The use of indirect paths in developing a channel model is impractical for large topologies with a long backbone and many indirect paths. In this thesis, a simple and flexible method is developed which can be used for any topology. A cell division (CD) method is implemented for a split-phase power system and the structure includes both 120 V single phase and 240 V split phase circuits. This structure is used in North American residences. The panel is fully described unlike the approaches in [18–20, 22–24]. Further, models for arc fault circuit interrupter (AFCI) and GFCI circuit breakers are presented. A bottom-up approach [25] is employed so the topology is modeled from the individual components. The advantage is that once a topology is modeled, it can be used to develop models for other topologies.
Indoor power lines were not originally designed for communication purposes, and the influence of electromagnetic noise can be considerable. It was stated in [10, 11] that noise will have a significant effect on the PLC performance, including the reliability and the quality of service (QOS), and so is a primary concern in PLC systems. At present, noise
Figure 1.2: An impedance carry back method [23] example.
analysis has focused on the network between SMs and DACs [13–16], whereas the HAN has had less attention. The power line channel cannot simply be considered as an additive white Gaussian noise (AWGN) environment [51]. Therefore, the noise modeling for HAN channels is challenging. The noise varies with frequency [26], and can be considered from broadband [27–30] or narrowband perspectives [31–34]. Further, most noise modeling has employed only measurement results in a top-down approach. However, this approach is based on empirical results that only fit a specific topology, while a bottom-up approach is general and can be used in developing a variety of models. Thus, a noise model using the latter approach is proposed for HANs.
1.2
Organization of the Thesis
The remainder of this thesis is organized as follows.
Chapter 2 provides an overview of PLC channel modeling. A wiring topology is charac-terized using North American residences and standards. The parameters of compo-nents in the topology are obtained to determine the impedances. These impedances are used to compute the transfer functions of PLC channels. The CD method for channel characterization is described in detail.
Chapter 3 uses the CD method to develop HAN channel models and is compared with other approaches in the literature. Models are given for three house sizes, small, medium and large with floor areas of 1000, 2000 and 4000 ft2, respectively. The smart meter is considered as the transmitter and modems in the branch circuits are
the receivers. Several branch circuits and breaker types are considered and their influence on the channel is examined. The CD method is implemented for a simple topology and the results are compared with those of existing methods.
Chapter 4 presents a HAN noise model which is comprised of background noise and im-pulse noise. The PSD of the noise at the receiver is obtained using the CD approach. The results obtained indicate that the proposed noise model is adequate for HANs. Chapter 5 provides some concluding remarks and suggestions for future work.
The Appendix presents the inner self inductance of circular and rectangular conductors considering the skin effect.
1.3
Contributions
This thesis contributes to the area of power line communications in the context of home area networks. A wiring topology is modeled for North American residences with a split-phase power supply. A smart meter is considered as the PLC transmitter or receiver, which is seldom discussed in existing channel models. The parameters of the topology components are found and their impedances are derived. The channel transfer functions are obtained using these impedances. A cell division method is developed for channel characterization. Compared to other channel modeling methods, the cell division is simpler and can be used to model any wiring topology including those that are large and complex. The channel model obtained is compared with those in the literature to verify its accuracy. A noise model is also developed using this approach, and the noise power spectral density (PSD) at the receiver is obtained and compared with an existing model. This represents a new means of PLC noise modeling.
Chapter 2
HAN Topology Modeling
Home wiring topologies can be used for PLC data transmission. They can be modeled based on the NEC and American Wire Gauge (AWG) [35] standards. In this chapter, the wiring topology of a single 2000 ft2 dwelling is developed. The parameters of the compo-nents within this topology are presented. A technique to model the topology is developed which can be used to obtain HAN channel models.
2.1
Wiring Topology
A home topology can be divided into three parts, the topology above the SM, the electrical panel up to the SM and the branch circuits. Figure 2.1 shows the topology above the panel. A secondary transformer delivers power to residences using a three-conductor service en-trance cable (SER) [17] with AWG 4/0 conductors. From this cable, a SER with AWG 2/0 conductors is connected to the panel through the meter. The SERs above and below the SM are labeled LB and LA, respectively. LAis between the smart meter and the junction with
the AWG 4/0 conductors that connects residences to the transformer. La1, La2 and La3 are
the conductors in LAthat correspond to phase one, neutral and phase two, respectively. LB
is between the smart meter and the panel where Lb1, Lb2 and Lb3 correspond to La1, La2
and La3.
The second part of the home topology is shown in Figure 2.2, which is a Homeline panel with a 200 A rating [36]. Lb1 and Lb3 connect the main breaker to the corresponding
hot bars, where 120 V single-pole and 240 V double-pole circuit breakers are placed and connected to phase conductors in the branch circuits. Lb2connects to a bonding strap which
Figure 2.1: The topology above the panel which includes the smart meter.
strap to a ground rod, so the neutral bars have zero potential. Both the neutral and ground conductors are connected to the neutral bars.
The third part of the home topology is the branch circuits. They are extended from the panel and deliver power to appliances. Modems are connected to outlets to provide information about the associated devices. AWG 6, 8, 10, 12 and 14 refer to the most commonly used conductors in home wiring which correspond to 50, 40, 30, 20 and 15 A branch circuits, respectively. An 80% ampere rating of branch circuits is used for safety operation. For instance, the maximum current in a 50 A circuit is 40 A. The minimum number and maximum length of branch circuits, number of outlets on a branch circuit and distance between the outlets are given by NEC either. Branch circuits are classified as individual, lighting and small appliance circuits as follows.
An individual circuit supports an outlet for one electric appliance which typically has large power consumption. Individual circuits can be either split-phase or single-phase. The former type supports high power electrical appliances such as a range, range top, washing machine, dryer, HVAC or water heater that are above 2000 VA. The latter type supports appliances with comparatively lower power consumption such as a range hood, dishwasher, waste disposal and trash compactor, but large initial power is necessary to start the motors inside the appliances.
Figure 2.2: The topology of a 200 A Homeline panel.
switches to control them. At least one switch controlled light is required in each habit-able room as well as bathrooms, hallways, stairways, garages, and storage or equipment spaces including attics, underfloor spaces, utility rooms, and basements. The floor area is calculated using the outside dimensions of the building to determine the required lighting power.
Small appliance (SA) circuits have multiple outlets for plug-in appliances other than those on individual circuits. These and all the other home appliances considered here are given in Table 2.1 [37]. They can be classified as resistive, reactive or linear periodically time varying (LPTV) (types 1 to 3, respectively) [25]. LPTV appliances have either com-muted (3-1) or harmonic (3-2) impedance variations. There are seven types of circuits (a to g), which are split phase individual circuits, single phase individual circuits, lighting circuits, kitchen SA circuits, bedroom, study and living room (BSL) SA circuits, laundry area SA circuits and bathroom SA circuits, respectively. Pr is the power consumed by the
Table 2.1: Appliance Parameters
Appliance Type Circuit Pr(VA)
Range 1, 2 a 8000 to 12000 Range top 1, 2 a 4000 to 6000 Range hood 2 b 70 to 240 Dishwasher 2 b 1200 to 1800 Waste disposal 2 b 300 to 800 Trash compactor 2 b 300 to 600
Dryer and washing machine 2 a 3000 to 5000
HVAC 2 a 2000 to 5000 Water heater 1, 2 a 2000 to 4000 Fluorescent lamp 3-1 c 20 to 100 Incandescent lamp 1 c 100 to 200 Live clock 2 d, e, f, g 5 to 15 Electric shaver 2 g 15 to 100
Smart phone charger 2 e 15 to 100
Blender 2 d 100 to 300 Stereo 3-2 e 100 to 300 Laptop 3-2 e 100 to 300 Plasma or LCD TV 3-2 e 100 to 300 Radio tuner 3-2 e 100 to 300 Humidifier 2 d, e, f, g 300 to 1000 Dehumidifier 2 d, e, f, g 300 to 1000 Refrigerator 3-2 d 300 to 1000 Percolator 1, 2 d 1000 to 1500 Toaster 1, 2 d 1000 to 1500 Potable kettle 1, 2 d 1000 to 1500 Iron 1, 2 e, f 1000 to 1500 Hairdryer 2 e, g 1000 to 1500
2.2
Modeling Branch Circuits and Above the Panel
PLC channels can be modeled using either a top-down approach or a bottom-up approach. Top-down channel models are based on parameters from extensive measurements [25]. S-ince wiring topologies differ, these results are typically not suitable for other channels. Further, measurement errors reduce the model accuracy. On the other hand, a bottom-up approach uses the actual wiring topology parameters to construct a model. Since the components can easily be changed, this technique is general and can be used for any topol-ogy [25]. In this section, a review of the component parameters is given. These parameters
and diameter of conductors in cables and strands in conductors, as well as the material and thickness of the conductor insulation. The p.u.l. resistance of a conductor R is derived from
R = ρ
A (2.1)
where the cross section area A is related to skin depth δ = √ 1
πµσf and f is the frequency. For a circular conductor with radius r, if δ ≥ r as in Appendix Figure A.1a, A = πr2. If
δ < r as in Appendix Figure A.1b, A = π[r2− (r − δ)2] = πδ(2r − δ). µ is the magnetic
permeability. For copper or aluminum, µ is equal to the vacuum magnetic permeability µ0 = 4π × 10−7 H/m. The conductivity σ is inversely proportional to the resistivity of
material ρ, which is 2.15 × 10−8Ωm for copper, and 3.45 × 10−8 Ωm for aluminum [35]. For simplicity, frequency dependent variables are expressed without the frequency variable, i.e. R(f ) is denoted as R. The p.u.l. resistance of a circular conductor is expressed as
R = 1 πσr2 when δ ≥ r, 1 πσδ(2r − δ) when δ < r, (2.2)
The copper conductors are used in modeling and the properties are given in Table 2.2. The number of conductors in a cable is used to infer the central distance of the paired conductors for the channel. In a 3-conductor cable, the central distance of two adjacent conductors is the diameter of a single conductor with its insulation. In a 4-conductor cable, the paired conductors can be in adjacent or diagonal positions [18], and the central distance in the first position is the same as the 3-conductor cable given the same conductors, and differs by a factor of √2 in the second position. The conductor insulation can be either polythelene or nylon polyamide and this determines the capacitance of the conductors. The insulation thickness and diameter of a bare conductor are used to infer the central distance of adjacent conductors. DC resistance values are used in voltage drop calculations to determine the length of conductors.
For conductors with more than one strand, i.e. 7 strands for AWG 3 and 6 and 19 strands for AWG 2/0 and 4/0 as shown in Figure 2.3, the current is concentrated in the outer ring of
Table 2.2: Properties of Conductors
Properties Cable type
XHHW SER NM-B
AWG 2/0 3 6 8 10 12 14
Number of conductors in cable 3 3 4 4 4 3 3
Material of conductor insulation Polythelene Nylon Polyamide
Relative dielectric constant ξr 2.3 2.55
Insulation thickness (mil) 55 45 35 35 24 19 19
Diameter of bare conductors (mm) 10.62 6.60 4.67 3.264 2.588 2.05 1.63 Strand diameter (mm) 2.13 2.20 1.56
Number of strands: total/outer ring 19/12 7/6 7/6
DC resistance (ohm/kft) 0.0967 0.245 0.491 0.764 1.21 1.93 3.07
Figure 2.3: AWG 6, 3 and 2/0 conductor strands.
strands. For these conductors, the resistance R is multiplied by a correction factor [40, 41]
XR= ne r2 scos −1 rs− δ rs − (rs− δ)prs2− (rs− δ)2 2rδ (2.3)
where the number of strands in the outer ring of conductors ne and strand radius rs are
given in Table 2.2.
For a pair of conductors, the inductance is
L = Lin+ 2(Lout± M ) (2.4)
is used in this thesis. If δ ≥ r, Lin=
µ
8π [38]. When δ < r, Linof a circular or rectangular conductor is given in the Appendix. If the conductor length l is much greater than the radius r and central distance d, then
Lout(l) = µ 2π log102l r − 1 (2.6) M (l) = µ 2π log102l d − 1 (2.7) and the inductance L is
L = µ πlog10 d r + µ 8π when δ ≥ r µ πlog10 d r + µ 8π(1 − (1 − δ r) 4) when δ < r (2.8)
In a homogeneous dielectric environment, the p.u.l. capacitance and reactance can be ob-tained from [40]
LC = µξ
LG = µσ (2.9)
where the dielectric constant is ξ = ξ0ξr, ξ0 = 8.859 × 10−12F/m is the vacuum dielectric
constant, and ξris the relative dielectric constant which is 2.3 for AWG 2/0 to 3 conductors
(polyethelene) and 2.55 for AWG 4 to 14 conductors (nylon polyamide). The p.u.l. param-eters are used to obtain the characteristic impedance Zcand propagation constant γ of the
conductors [23] Zc= s R + jωL G + jωC, γ = p (R + jωL)(G + jωC) where ω = 2πf .
The end of a conductor furthest from the transmitter is called the input while the other end is called the output. The input impedance of a conductor Zin is determined by the
impedance of all components at the input of the conductor. For instance, if the conductor is between an outlet and an appliance which is on, the impedance of the appliance is the input impedance. If the appliance is off or the outlet is open (i.e. no appliance), then Zin=
∞. If Zin is determined by N parallel impedances Z1, Z2, . . . , ZN, i.e. at the junction of
several conductors or at an outlet with a modem and an appliance, then 1 Zin = 1 Z1 + 1 Z2 + · · · + 1 ZN . (2.10)
NEC places limits on conductors in branch circuits [17] including the gauge of conduc-tors, ampere rating of branch circuits, minimum number and maximum length of branch circuits, number of outlets on a branch circuit, and distances between outlets. The length of a branch circuit should accommodate a maximum 3% voltage drop [35]. For individual circuits, the voltage drop Vdof a conductor is [42]
Vd= 2RsLsI, (2.11)
where Rs is the p.u.l. DC resistance of the conductor given in Table 2.2. The minimum
length is Lmin = 6 ft [37], and the maximum length Lmax should be less than 100 ft.
The maximum current Imax is 0.8 times the amperage rating of the corresponding circuit
breaker. Lmax can be obtained from (2.11) considering the maximum voltage drop. For
lighting and small appliance circuits [21]
Vd= 2Rs N
X
n=1
lnIn, (2.12)
where N is the number of outlets. The maximum number of outlets is Nmax =
Imax
1.5 where the rated current of each outlet is 1.5 A [35]. The furthest outlet from the circuit breaker corresponds to n = 1, and lnis the length of the conductor between outlets n and n + 1, or
between outlet N and the circuit breaker [17]. In = 1.5 × n. NEC recommends that for a
branch circuit, the distance from the circuit breaker to the closest outlet should not exceed 70 ft for an AWG 12 conductor (SA circuit), or 50 ft for an AWG 14 conductor (lighting circuit). The recommended distance between outlets is 0 to 12 ft.
The output impedance of a conductor is [24]
Zout = Zc
Zin+ Zctanh (γl)
Zc+ Zintanh (γl)
Appliance impedances are the input impedances of the corresponding outlet conductors and are obtained as follows [25]. Resistive type appliances have negligible reactive impedance, so their impedances are constant values. Typical resistive appliances are heating loads such as an electric range, range top, water heater and electric kettle. The reactive components of these appliances, such as coils in small LEDs, are inductances smaller than 10−2 µH. An incandescent lamp has a coil inductance smaller than 1 µH. The impedance of resistive loads is
Zapp =
U2
Pr
, (2.15)
where U = 120 V for single phase and U = 240 V for split phase circuits.
Reactive type appliances have frequency-selective impedances. This includes inductive heating and appliances with motors such as hairdryers and air conditioners. The impedance of reactive loads is obtained from the parallel RLC circuit model [25] as
Zapp= Rs 1 + jQf ω ω0 − ω0 ω (2.16) where Rs = U2 Pr
is the resistance at resonance. The quality factor Qf is an indication of
frequency selectivity and is typically between 5 and 25. The resonant frequency f0 =
ω0
2π is between 25 kHz and 200 kHz [43, 44].
Linear periodically time varying type appliances have frequency-selective and time varying impedances. This includes fluorescent lamps, radio tuners, computers and smart TVs. The impedance variations of LPTV loads are caused by non-linear elements such as thyristors. These appliances can be described using the series linear time invariant (LTI) model given in [25].
A secondary transformer is included in the HAN model. It is connected to residences by overhead and underground SERs. In [45], impedance measurements of secondary trans-formers with capacities from 10 kVA to 50 kVA were given. From these results, the
sec-ondary transformer impedance is
Zt= Rt+ jXt, (2.17)
where at 0 Hz, Rt is between 0 and 1 Ω and Xt is 0 Ω, and Rt and Xt increase with
frequency at rates from 0.054 to 0.081 Ω/kHz and 0.4 to 1 Ω/kHz, respectively.
2.3
Modeling the Topology Inside the Panel
The conductors in the panel are modeled differently than in the rest of the topology because of their structure. In branch circuits and the topology above the panel, the conductors are closely packed in cables with the phase and neutral conductors sealed by insulation. The length l of these conductors is far greater than the cross section dimensions r and d. In the panel, the conductors are further apart and can be circular or rectangular. The latter type comprises bars and the bonding strap, which are not sealed, and the cross section dimensions are comparable to the lengths. The p.u.l. impedance of a conductor in the panel is
Zcp = Rcp+ jXcp, (2.18)
where Rcp is the p.u.l. resistance. For circular conductors, Rcp is the same as in branch
circuits. For the rectangular case [46]
Rcp= 1 σW T when δ ≥ min(W, T ), 1 2σδ(W + T − 2δ) when δ < min(W, T ), (2.19)
where W and T are the width and thickness of the conductor, respectively. The imaginary part of Zcp is Xcp = 2πf Lcp where Lcp = Lin + Lout is the p.u.l. inductance. The
corresponding TF is
Hcp =
Zin
Zin+ Zcp
. (2.20)
The parameters of the rectangular conductors are summarized in Table 2.3.
Homeline thermal magnetic breakers are widely used in North America and are referred to as normal breakers. Three Homeline breakers are shown in Figure 2.4a and Figure 2.4b, which shows a 200 A main breaker and 30 A and 20 A circuit breakers, respectively. In the past 20 years, advanced Homeline AFCI or GFCI breakers have been developed to provide
Neutral bar 0.3125 0.4375 0.3125 (central distance between slots)
Bonding strap 1 0.25 9
fault current detection and protection [47–49]. In [22], circuit breakers with various am-pere ratings were modeled, but only single-pole normal breakers were considered. In this thesis, both single-pole and double-pole, normal and advanced Homeline circuit breakers are modeled.
Figure 2.5 shows the general model for a Homeline breaker. The normal breaker struc-ture is shown on the left of the dashed line and includes a bare copper wire, a bimetallic strip using alloys of copper and steel, and a single copper strip. The bare copper conductor has a radius r determined by the breaker amperage and the length l is 2 in. The width and length of the strips are 0.5 and 1.75 in, respectively. In the main breaker, their thickness is 0.08 in, which in branch circuit breakers is 0.04 in. An AFCI or GFCI breaker includes the right part with coils and two conductors. One conductor of length 1.75 in connects the single copper strip to the phase conductor of the corresponding branch circuit. The other conductor of length 17.5 in connects the neutral conductor to the neutral bar. In an AFCI breaker, sensing coils T1 and T2 detect series and parallel arcing caused by loose connec-tions and broken conductors, respectively. A GFCI breaker only has a T2 coil to detect parallel arcing. A double-pole circuit breaker can be considered as two parallel single-pole breakers. For AFCI or GFCI double-pole breakers, three conductors are used and mon-itored by the T1 and T2 coils. The impedance and transfer functions of the conductors within these breakers can be obtained using (2.13) and (2.14), or (2.18) and (2.20) with the parameters above.
2.4
Cell Division Method
In this thesis, the cell division method is introduced as an efficient means of modeling HAN topologies. This approach divides a topology into cells and determines the corre-sponding impedances and transfer functions. The appliances, modems and SM, conductors and secondary transformer are considered as basic components of the topology, and a cell
(a)
(b)
Figure 2.5: The circuit breaker model.
is comprised of several basic components. Each cell comprises only one junction, which is a node with three conductors. The conductors are divided into two groups, junction to junction (J-J) and junction to unknown (J-U). A cell comprises a junction, J-J and J-U con-ductors, and other components. A J-J conductor connects the cells of adjacent junctions. A J-U conductor is between a junction and other components such as an open outlet, an appliance with a modem, a single appliance, the smart meter, or another J-U conductor.
The CD method consists of the following steps. Once the topology is obtained, cells are defined and categorized into three types according to the conductors at the junctions. The first type are cells with one J-J and two J-U conductors such as those at the ends of the branch circuits. The second type are cells with two J-J and one J-U conductors such as those in the remainder of the branch circuits. The third type are cells with three J-J conductors such as those in the panel. Next, the Tx and Rx locations are determined which can be in the first and second types. The inputs and outputs of all the conductors are then determined. As shown in Figure 2.6, the impedance computation for cells is carried out following a bottom-up approach. For branch circuits without the Tx, the computation is from the first type cells to the third type cells (in the panel). The topology above the panel is similar to a branch circuit where the smart meter can be a Tx or Rx. For the branch circuit with the Tx, the computation continues to the Tx cell and ends when the output of the J-U conductor to the Tx is obtained.
Figure 2.6: Impedance computation directions of the CD method.
using the corresponding impedances. The TF of paired conductors uses (2.14), whereas (2.20) is employed for single conductors in the panel. The TFs of the J-U and J-J conductors are denoted by HJ −U and HJ −J, respectively. Then
Hb = HJ −U(1) Nc−1 Y i=1 HJ −J(i) ! HJ −U(Nc), (2.21)
where i = 1 corresponds to the Rx cell and Ncis the number of cells in the direct path
be-tween the Tx and Rx. Next, the topology above the panel is considered as shown in Figure 2.1. If Lb1 and Lb2 are used which correspond to phase one and neutral, then the output
impedance Zbis obtained as the impedance of the current residence. The impedances Zbof
other residences are obtained using the same approach with a random but similar topology. Using this topology, the output impedance Za of LA can be inferred using (2.13) which
represents the impedance of the topology above the SM. The TF of the topology above and including the SM is
Has =
Za k Zb
Za k Zb+ Zsm
, (2.22)
where k denotes that the two impedances are in parallel, Zsm is the impedance of the smart
meter, which is the modem impedance assumed to be 50 Ω [25]. The TF for the complete topology is then
Ht= Hb× Has. (2.23)
con-outlet as a J-U conductor, and modeled with l2using the steps between the ∗ in Figure 2.8.
Otherwise, l3 is a J-J conductor so the input impedance of l3 is obtained from the cell at
its input. When the impedances of these conductors are obtained, the inputs of conductors l2 and l3 are examined to see if the Rx is present. If the Rx is at the input of l2 or l3, then
it also an input of l4, so the TFs of l2 and l4, or l3 and l4 are obtained. If there is no Rx,
then only the impedances are necessary. Cells in the remainder of the topology are then modeled in turn using the same procedure. A simple topology which has been divided into cells is shown in Figure 2.9. For the given five cells, the impedance is computed rightwards in a bottom-up approach. In the process, only the TFs of denoted U-J and J-J conductors are computed.
Chapter 3
Model Analysis And Validation
To obtain a channel model for a topology, a database of component parameters is used which includes the characteristic impedances and propagation constants of conductors, cross section areas of conductors in branch circuits, and the dimensions of the conduc-tors in the panel. The IEEE low-frequency NB-PLC standard [11] for smart applications specifies a frequency band from 3 kHz to 500 kHz. The frequency-dependent parameters are determined for 256 discrete values uniformly distributed between these frequencies. In a topology, the SM is assumed to be the Tx and the Rx is a modem on a branch circuit. The TFs are determined for the channels to all modems in the topology.
3.1
Topology Parameters
All random parameters are obtained using a uniform distribution. The branch circuits are considered first and the appliances connected to them are either on or off with independent probabilities of 0.5. The lighting circuits are determined by the floor area. Consider a medium size house with a floor area of 2000 ft2. According to NEC, the minimum lighting required is 3 VA/ft2, so the minimum lighting load is 6000 VA. Lighting circuits are 120 V and 15 A, so the maximum load is 15 × 80% × 120 = 1440 VA where the 80% load rating is for overcurrent protection. The rating of an outlet is 180 VA, so there can be 1440/180 = 8 outlets on a circuit. Thus 4 lighting circuits are required and AFCI breakers recommended. Another circuit with 4 lights for 2 bathrooms is assumed and in this case GFCI breakers recommended. Each light switch controls a fluorescent or incandescent lamp with equal probability.
SA circuits correspond to circuit types d to g in Table 2.1 and each supports a maximum of (20 × 80% × 120)/180 ≈ 10 outlets for low power appliances. NEC suggests at least two circuits for kitchens, plus one for the laundry area and one for bathrooms. In the medium house model, two SA circuits each with 10 outlets are in the kitchen, and each bathroom and laundry circuit has 4 outlets. These are wet environments, so GFCI breakers are recommended. There are 8 different appliances which can be located on the two kitchen SA circuits, 3 on the laundry SA circuit and 4 on the bathroom SA circuit. Four bedrooms, a living room and a study are assumed with 5, 10 and 5 outlets in each room, respectively, which requires 4 SA circuits. There are 10 different appliances which can be located on these circuits. A TV, laptop and smart phone charger are randomly positioned in each room with independent probabilities of 0.5. One live clock is placed on a random SA outlet in the house. Further, one humidifier or dehumidifier with equal probability of 0.5 is randomly located on an SA circuit. An iron is located on a laundry or BSL SA circuit and a hair dryer is located on a bathroom or BSL SA circuit. The parameters for small, medium and large house sizes including the numbers of appliances are given in Table 3.1.
Within the panel, the circuit breakers are placed evenly on both sides of the hot bars starting from the top. The length of the cable (AWG 2/0) between the panel and the SM is between 6 ft and 10 ft. The cable (AWG 2/0) between the SM and junction to the transformer cable (AWG 4/0) is between 40 ft and 50 ft. There are between 5 and 20 residences randomly located on the transformer cable with from 50 ft to 70 ft between them. The secondary transformer is randomly located on the AWG 4/0 cable.
3.2
Channel Modeling and Analysis
The insertion loss (IL) can be expressed as
IL = 20 log10|Ht| , (3.1)
where Htis obtained from (2.23).
To better illustrate the impact of the topology components, first only normal breakers are considered. AFCI and GFCI breakers will be employed later. MATLAB was used to
Table 3.1: Parameters for the Three House Sizes
House size Small Medium Large
Floor area (ft2) 1000 2000 4000
Length of the branch circuits (ft) 6 - 80 6 - 100 6 - 150
Number of lighting circuits 4 5 10
Number of bathroom lights 2 4 6
Number of BSL SA circuits 2 4 6
Number of kitchen SA circuits 2 2 3
Number of laundry SA circuit outlets 2 4 6
Number of bathroom SA circuit outlets 2 4 6 Number of kitchen appliances 5 to 7 5 to 7 5 to 7
Number of BSL appliances 14 to 18 20 to 24 29 to 33 Number of laundry appliances 0 to 2 0 to 3 0 to 3 Number of bathroom appliances 1 to 2 1 to 4 1 to 4
HVAC 1500 to 2000 to 3000 to
3000 VA 5000 VA 7000 VA
Refrigerator 200 to 300 to 500 to
800 VA 1000 VA 1500 VA
obtain the transfer functions for 1000 random topologies of each of the small, medium and large house sizes. The execution times were 233 s, 322 s and 382 s, respectively. The average IL of the TFs for each size are given in Figure 3.2 and summarized in Table 3.2. The IL is highest for frequencies close to 0 kHz but decreases rapidly with frequency. The IL is lowest at 500 kHz, and fluctuates in the remaining frequency spectrum. The average IL of the small house is approximately 5.9 dB better than the medium house and 7.6 dB better than the large house. Thus, both the frequency and topology have a significant influence on the IL, and the larger the house the higher the IL.
Only the medium house is considered in the remainder of this chapter. Figure 4.4 shows the ILs of 15 different channels from two random medium house topologies. Although the magnitude varies, the channels have similar peaks and notches at certain frequencies. This is due to the same components within a topology. A home topology can be divided into three parts, the branch circuits, the panel up to the SM, and the SM and above. To better understand their effect on the channel, the average IL for each part is given in Figure 3.3 and summarized in Table 3.3. This indicates that the topology above the SM significantly affects the IL.
SA circuits and individual circuits are now compared. The average IL of the SA and individual circuit channels is shown in Figure 3.4. The average IL difference is between
(a)
(b)
Figure 3.1: The IL of 15 channels from two different medium size house topologies. Table 3.2: Average IL for the Three House Sizes
Size Minimum (dB) Maximum (dB) Mean (dB)
Small -77.31 -53.41 -59.64
Medium -83.60 -59.30 -65.50
Large -84.67 -60.71 -67.25
−17.0 dB and −8.8 dB with a mean of −14.4 dB. This difference is due to the SA circuits having multiple outlets whereas an individual circuit has only one outlet. The effect of
Figure 3.2: The average IL of the channels in the 1000 topologies for each house size.
normal and advanced circuit breakers is now examined. The average IL using only normal breakers and using AFCI and GFCI breakers as recommended by NEC [35] is shown in Figure 3.5. The difference is between −7.7 dB and −2.7 dB with a mean of −5.9 dB. This is principally because the advanced breakers have additional neutral conductors used for detecting fault currents that influence the IL.
Figure 3.4: The average IL of the 9000 individual circuit channels and the 8000 SA circuit channels in the 1000 topologies.
3.3
Comparison of Channel Models
The Ca˜nete wiring topology is a simple topology with 3 appliances as shown in Figure 3.6a [25]. This was modeled using the ABCD matrix method in [50]. The values of A, B, C and D for a conductor can be obtained from the p.u.l. R, L, G and C parameters,
Figure 3.5: The average IL with normal breakers and AFCI and GFCI breakers.
frequency f and length l. The parameters of appliance i, i = 1, 2, 3, are given in Table 3.4 and the corresponding impedances |Zi| are shown in Figure 3.7.
Table 3.4: Parameters for Three Appliances
Appliance Parameters
Power Pr (VA) Resonant frequency f0(kHz) Quality factor (Qf)
1. Stereo 243.0 161.3 9.0
2. Laptop 248.8 30.3 17.4
3. TV 261.1 175.4 5.6
At junction Ji, the output impedance of conductor Li is given by
Zouti =
AiZi+ Bi
CiZi+ Di
(3.2) so the ABCD matrix of the topology between the source ZS and load ZLis
A B C D = A(3,S) B(3,S) C(3,S) D(3,S) 1 0 1/Zout3 1 A(2,3) B(2,3) C(2,3)D(2,3) 1 0 1/Zout2 1 A(1,2) B(1,2) C(1,2) D(1,2) 1 0 1/Zout1 1 AL BL CL DL. (3.3)
(a)
(b)
Figure 3.6: The Ca˜nete wiring topology modeled using (a) the ABCD matrix method, and (b) the cell division method.
This can be used to obtain the transfer function HT. Without considering ZS [24]
HT =
ZL
AZL+ B
(3.4) With the proposed method, there are three cells in the topology given in Figure 3.6a, as shown in Figure 3.6b. The impedance computation starts from cell 1 and proceeds to cell 3. The TFs of conductors HJ −U(1), HJ −J(1), HJ −J(2), HJ −U(3) were obtained and are
Figure 3.7: The impedances of the three appliances.
the same IL as HT obtained from (3.4) as shown in Figure 3.9. On the other hand, the
proposed method is flexible in modeling complex topologies, whereas the ABCD matrix method is not an efficient means for real applications as it uses one matrix to represent the entire topology which is impractical.
Figure 3.8: The TFs of four conductors.
Chapter 4
Noise Characterization
A widely accepted power line noise model characterization was given in [51], in which the noise is classified into 5 groups as shown in Figure 4.1. This indicates that the noise is complex and cannot be described as just AWGN. These 5 groups can be further cate-gorized as background noise or impulse noise. The root mean square (RMS) amplitude of the narrowband interference and colored noise varies slowly over time, so they are called background noise [27, 52]. Narrowband interference comprises mostly modulated sinu-soidal signals caused by ingress of signals from broadcast stations. Colored noise is mainly the sum of numerous noise sources with low power [53]. For instance, colored noise can be generated by a TV receiver power supply, or a malfunctioning demodulator within the TV. Electrical ballasts within home appliances such as fluorescent lamps also create colored noise. The impulse noise includes 3 groups, namely periodic impulse noise which is syn-chronous or asynsyn-chronous to the voltage frequency, and asynsyn-chronous impulse noise which is not periodic. Periodic impulse noise asynchronous with the voltage is mostly generated by switched-mode power supplies (SMPSs). Periodic impulse noise synchronous with the voltage is mainly caused by switching of silicon rectifier diodes with short duration (ms) and has a PSD decreasing with frequency. Asynchronous impulsive noise is caused by switching transients or the connection and disconnection of home appliances [30], both of which have a short duration (ms).
The impulse noise can be modeled as in Figure 4.2. The impulse noise sources and the receiver are located in different places in the topology. Within the frequency range 3 to 500 kHz, the dominant noise is background noise and periodic impulse noise asynchronous with the voltage [28, 54]. This chapter aims at modeling the latter which requires the channel model obtained from the topology.
Figure 4.1: The classification of PLC noise [51].
In [27], A noise model was proposed which can be expressed as Ssm= Sbk(f ) + N X i=1 [Si(f ) × |Hi(f )|2] dBm/Hz (4.1)
where Sbk(f ) denotes the background noise, and Si(f ) and Hi(f ) are the impulse noise at
the ith source and the transfer function of the channel between the ith source and receiver, respectively. Each source contributes to the noise PSD at the receiver and there are N sources. According to [28], 95 of 100 measured appliances are driven by SMPSs, which are the main impulse noise sources.
4.1
Noise Modeling Examples
The modeling of background and impulse noise is now considered.
4.1.1
Background Noise
The background noise can be modeled in the time domain or frequency domain. A typical time domain model for background noise was given in [27]. The background noise in the frequency domain is given by [17]
Sbk = a + b|f |c dBm/Hz (4.2)
where a, b and c are as follows [54]. The parameter a has a truncated normal distribution within three intervals as in Table 4.1. This table includes the mean, standard deviation (std) and probability of a in each interval. The parameter b has a lognormal distribution with mean 12.95 and standard deviation 4.42 while c has a normal distribution with mean -0.94 and std 0.49.
Table 4.1: Distribution of a
Mean Standard deviation (std) Probability
−120 ≤ a < 0 105.07 4.70 0.66
−200 ≤ a < −120 142.71 21.51 0.29
a < −200 656.41 619.16 0.05
The frequency f is between 3 kHz and 500 kHz. Within these frequencies, Sbk has
and the parameters above. The curves representing the best and worst cases are shown in Figure 4.3. The parameters a, b, and c are (-146.9608, 589.2164, -0.3881) in the best case and (-129.5523, 1.4002 × 104, -0.9301) in the worst case, respectively.
Figure 4.3: The best and worst cases of background noise.
4.1.2
Impulse Noise
A low voltage indoor power line noise model for impulse noise at the receiver was given in [54] SN(f ) = N X i=1 aiexp −(f − fi) 2 2σ2 i dBm/Hz (4.3)
where N is the number of impulse sources. ai is the amplitude of the impulse noise at the
receiver, which follows a Gamma probability density function (PDF) f (x; α, β) = 1
βαΓ(α)x α−1
where
Γ(α) = Z ∞
0
tα−1e−tdt (4.5)
is a Gamma function with α = 2.79 the shape parameter and β = 5.34 is the scale pa-rameter. fi is the center frequency of the ith impulse signal, which has a truncated normal
distribution within five frequency intervals as given in Table 4.2. This table includes the mean, standard deviation and probability of fi within each interval.
Table 4.2: Distribution of fi
Range (kHz) Mean (kHz) σi (kHz) Probability
3 ≤ fi ≤ 100 55.90 22.11 0.27
100 < fi ≤ 200 144.00 24.89 0.20
200 < fi ≤ 300 258.61 29.75 0.21
300 < fi ≤ 400 346.74 26.81 0.18
400 < fi ≤ 500 453.15 30.18 0.14
In this chapter, the impulse noise at the Rx is obtained from [27] as
Ssm = N
X
i=1
[Si× |Hi|2] dBm/Hz (4.6)
where Si is the impulse noise at the ith source which is given by
Si = Aiexp −(f − fi) 2 2σ2 i (4.7)
where the amplitude Ai is obtained using
Ai =
|Ui|2
|Ri|
(4.8)
where Ui is the voltage of impulse noise at the source given in Table 4.3 [56] and Ri is the
load impedance.
Table 4.3: Impulse Noise Parameters Mean (V) Std (V) Min (V) Max (V)
0.0301 0.0133 0.0141 0.0495
The models (4.3) and (4.6) are now compared. A medium size house is now considered and the appliances in the topology are as follows. The 9 individual circuits include 9 plugs
appliances in the topology. A random medium size home topology is now obtained with 43 appliances turned on. Thus there are N = 43 impulse noise sources. For each source, fi and σi are obtained using Table 4.2. For the impulse noise model (4.3), the amplitude
ai of each source is obtained using (4.4). For the proposed impulse noise model (4.6), the
amplitudes Ai are obtained using the truncated Gaussian distribution given in Table 4.3
and the transfer functions between the 43 appliances and smart meter are obtained from the home topology. Two noise models are obtained using (4.1) with the corresponding PSDs given in Figure 4.4a and cumulative distribution functions (CDFs) in Figure 4.4b. Altogether 27 impulse noise peaks are observed (less than 43), indicating that some peaks with close center frequencies merged. The PSD differences between the two noise models at these peaks are given in Table 4.4 where the minimum is 0.76 dBm/Hz at 170.62 kHz, and the maximum is 20.92 dBm/Hz at 180.36 kHz.
Table 4.4: Power Spectral Density Differences Between (4.3) and (4.6) at the Impulse Noise Peaks f (kHz) 20.54 40.03 59.52 75.11 82.91 86.81 104.35 PSD (dBm/Hz) 9.14 2.17 11.20 3.59 8.63 7.24 2.57 f (kHz) 110.20 121.89 170.62 180.36 199.85 213.49 236.88 PSD (dBm/Hz) 6.19 10.47 0.76 20.92 1.51 6.86 4.10 f (kHz) 248.58 256.37 260.27 293.40 310.95 314.84 334.33 PSD (dBm/Hz) 4.41 7.22 5.99 1.77 4.97 4.01 12.92 f (kHz) 355.77 367.47 379.16 441.53 461.02 468.82 PSD (dBm/Hz) 3.46 11.01 8.30 9.90 11.66 4.05
(a)
(b)
Chapter 5
Conclusions
In this thesis, power line communication (PLC) channel models were developed for a home area network (HAN). The thesis started with an introduction to smart meters (SMs), includ-ing the services they provide and the standards associated with PLC. PLC based research was introduced and a literature review of PLC HAN channel modeling was given. Noise modeling was also discussed.
In Chapter 2, the wiring topology of a split-phase power system was modeled in detail. It has three parts, the topology above the SM, the electrical panel up to the SM and the branch circuits. The parameters of the components within the topology were provided. These components are conductors, appliances, modems, the smart meter and the secondary transformer. A cell division (CD) method was proposed to obtain a channel model using this topology. This approach uses the actual parameters of the topology components and thus provides an accurate model.
Chapter 3 presented results for random topologies. Three topology sizes, normal break-ers and advanced breakbreak-ers, the three parts of the topology, as well as individual and small appliance (SA) circuits were considered. The CD method was shown to be an efficient means of modeling HAN topologies. This method was used to develop a model for the Ca˜nete wiring topology which is well-known in the literature. The results indicate that the CD method provides accurate channel models. This method can also be used to obtain channel models for other electrical systems such as in an electric vehicle or a solar panel, and for any building topology.
A noise model for a HAN PLC channel was developed in Chapter 4 which is comprised of background and impulse noise. The impulse noise at the receiver was obtained using the channel transfer functions (CTFs) between the impulse noise sources and the receiver, and the impulse noise at the sources. This model was compared with the literature which
shows good agreements in the PSDs and CDFs of the models. These results indicate that the proposed model is suitable for modeling noise in HANs.
The following topics are suggested for future work. The receiver side bit error rate (BER) can be obtained for performance evaluation of PLC in the HAN using the pro-posed models. In the physical (PHY) layer, different modulation schemes can be compared to find the most appropriate solution. In the medium access control (MAC) layer, CS-MA, CSMA/CA and TDMA can be evaluated to determine which of the contention and contention-free mechanisms is appropriate for SG applications. From the perspective of noise modeling, the impulse noise generated in electrical switch and thermostat on and off events, electrical plug insertion and removal and electrical engine start events [56] were not covered in this thesis. The influence of these transient events is a promising topic for future PLC research.
Appendix A
The Inner Self Inductance of a Circular
or Rectangular Conductor
The inner self inductance without considering the skin depth is given in [38]. In this ap-pendix, the p.u.l. inner inductance with skin effect is discussed. Consider a circular con-ductor as shown in Figure A.1a with a skin depth greater than the radius. The magnetic flux in the circle with radius rcis
(a) (b)
Figure A.1: Circular conductors when (a) the skin depth is greater than the radius, and (b) otherwise. I B × dl = µI ×rc r 2 where B = µIrc 2πr2. (A.1)
The magnetic field energy is 1 2µ Z B2× dV = 1 2LI 2 (A.2)
(a) (b)
Figure A.2: A rectangular conductor when (a) the skin depth is greater than half the smaller of the width W and depth T , and (b) otherwise.
where dV = rcdrcdθdZ. The inner self inductance is
Lc,in = µ 4π2r4 Z 1 0 dZ Z 2π 0 dθ Z r 0 r3cdrc= µ 8π. (A.3)
Figure A.1b shows that when the skin depth is much smaller than the radius
Lc,in = µ 4π2r4 Z 1 0 dZ Z 2π 0 dθ Z r r−δ r3cdrc= µ 8π " 1 − 1 − δ r 4# (A.4)
For a rectangular conductor with a skin depth greater than half the smaller of the width W and depth T , as shown in Figure A.2a, the current flows in the entire cross section area. The magnetic flux in the rectangle with side lengths a and b is
I B × dl = µI × ab T W (A.5) where a = 2xT D and b = 2xW D , which gives B = µIx D(T + W ) (A.6)
in which D =√W2+ T2. The magnetic field energy is
1 2µ Z B2× dV = 1 2LI 2
so
Lc,in =
µ√W2+ T2
16(W + T ) (A.8)
When the skin depth is less than half the smaller of the width W and depth T , as shown in Figure A.2b, the magnet flux in the rectangle with width b + 2x and depth a + 2x satisfies
I
B × dl = µI × 2ax + 2bx + 4x
2
2aδ + 2bδ + 4δ2 (A.9)
where a = T − 2δ and b = W − 2δ, which gives
B = µI × 2ax + 2bx + 4x
2
2aδ + 2bδ + 4δ2 ×
1
2(a + b + 4x) (A.10)
The magnetic field energy is 1 2µ Z B2× dV = 1 2LI 2
where dV = 2(a + b + 4x)dx so that 1 2µ Z δ 0 µI ×2ax + 2bx + 4x 2 2aδ + 2bδ + 4δ2 × 1 2(a + b + 4x) 2 × 2(a + b + 4x)dx = 1 2LI 2 (A.11) L = µ (2aδ + 2bδ + 4δ2)2 1 2x 4 + 1 2(a + b)x 3− 1 16(a + b) 2 x2 +1 32(a + b) 3x − 1 128(a + b) 4ln (a + b + 4x) δ 0 (A.12)
Then the inner inductance is Lr,in= µ 2δ2(W + T − 2δ)2 δ4 4 + δ3 4(W + T − 4δ) − δ2 32(W + T − 4δ) 2 + δ 64(W + T − 4δ) 3− (W + T − 4δ)4 256 ln W + T W + T − 4δ . (A.13)
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